Students often worry about the time it takes to finish exam. Suppose that the completion time in hours, T, for final exam follows a distribution with density

f(t) = (2/9) * (3t-t^2), 0 <= t <= 3.

1) what is the probability that a randomly chosen student finishes the exam before the final hour of the exam? P(0

2) what is the probability that a randomly chosen student finishes the exam during the final hour of the exam?

3) if 10 students are selected at random, what is the probability that exactly 7 of them finish the exam before the final hour of the exam?

4) calculate the expected value of the time it takes to finish the final, E[T]

5) calculate the median time, median[T].